You won't (write software to) do that without knowing a whole bunch of linear algebra and ODEs.
The fortune-telling part is not what needs the math degree.
The sign that a planet is in, which house, and aspects between the planets are what enables astrological fortune-telling and prediction (the forecasting aspect of astrology is technically known as transits and progressions, this is the "predicting the future" piece).
The bedside manner of the astrologer obviously has an enormous influence. One astrologer will look at a chart and treat it as a fixed "you are this way because of your chart" as if you can't change. A more thoughtful (read: actually good) astrologer will treat the chart as an evolutionary blueprint for growth and change. In many ways astrology is really just a different version of psychology and counseling.
A great book to read if you're open-minded but also don't want a bunch of "woo" is to check The Inner Sky by Steven Forrest. The first chapter of the book is called "Why Bother?" For what it's worth I had my chart read by Steven and it has really helped me in my life.
So? The people who believe astrology readings would believe them even if the maths is wrong.
The readings themselves don't match outcomes anyway, so it's not like the buyers of readings can even tell that the maths was wrong!
The average Visual Basic programmer and the world's best mathematician are going to be about equally good at writing the fortune-telling part, but the mathematician will have a much easier time getting the factual part right.
Alright, you're on - post the place you were born, including date and time and I'll cast your chart and tell you what I see. Then you can tell me if you think it's bullshit or not.
Free reading, you have nothing to lose.
Example: Milpitas, CA @ 4:52am January 24 1987
I see what you did there
The "whale" users who account for a disproportionately large percentage of an astrologer's revenue tend to know the factual information surrounding their birth fairly well. An app/astrologer who doesn't get these facts right, even for a handful of clients, will get a bad reputation fairly quickly.
I reckon the same principle would hold in cultural bubbles where reading tea leaves is a customary means of divination. If the client recognizes recognize black tea, but the fortuneteller insists it is rooibos, there won't be much trust in the rest of the prophecy.
Advertising that the horoscope shop uses Haskell is actually a solid business idea. It pre-filters for the sort of dev who will be able to do the math.
My impression (not interested in pseudo sciences so I haven't looked into this hard) was that Astrology froze before Kepler explains how the planets move, and so the model used by astrologers is just wrong and won't actually tell you what was in the sky when you were born for example?
You don't need Newton (who figured out why they do that) but you do need Kepler or your physical data will be wrong surely? It won't matter because this isn't actually a way to divine the future, but it will be wrong AIUI
Modern ascendant calculations are "correct", in the sense that they'll match what you see in the sky. Apps like AstroMatrix work from NASA data.
As you rightly observed, it doesn't make a difference when it comes to foretelling the future. But it does make a difference if your aim is to make money selling it. The big spenders on these applications often care a great deal about getting the particulars just so.